Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22625834 | C2 | semidirect |
| 3. #22625831 | C2 | semidirect |
| 5. #22624833 | C2 | semidirect |
| 6. #22624802 | C2 | semidirect |
| 26. #17988920 | C4 | semidirect |
| 28. #17988906 | C4 | semidirect |
| 29. #17988905 | C4 | semidirect |
| 34. #484×C73 | C4 | semidirect |
| 240. C73 | #9522 | semidirect |
| 244. #484 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626802 | 2 |
| #22625834 | 2 |
| #22625831 | 2 |
| #22625349 | 2 |
| #22624833 | 2 |
| #22624802 | 2 |
| #22619858 | 2 |
| #9522 | 73 |